Critical current versus transverse stress and thermal stability of a RRP Nb3Sn Rutherford cable

Critical Current versus Transverse Stress and Thermal Stability of a RRP Nb ₃ Sn Rutherford Cable.

Master assignment report within the MSc. Program Applied Physics carried out within the research chair Energy, Materials and Systems at the University of Twente.

Author: W. van de Camp Supervisor: Dr. M. Dhall´ e

Date: November 16, 2012

Examination Committee:

Prof. dr. ir. H.J.M. ter Brake

Prof. dr. ir. H.H.J. ten Kate

Dr. ir. H. Wormeester

Dr. M. Dhall´ e

Abstract

A full-sized state-of-the-art superconducting Nb 3 Sn Rutherford cables was tested in terms of its critical current up to a magnetic peak field of 12 T and transverse stress levels up to 270 MPa.

Also its thermal stability was assessed as function of magnetic field and test current over a field range of 2 to 11 T and currents from 7 to 20 kA. These measurements were preformed on a cable intended for the DS magnet, which constitutes an important first step in the LHC upgrade program. The samples were tested over a length of 45 mm on a U-shaped sample holder powered by a superconducting transformer. The cable was validated for the application in the DS magnet, both in terms of cabling degradation and in terms of operational transverse stress.

Irreversible reduction of the critical current only occurs at transverse stresses far above the

maximum coil stress expected in the DS magnet. The transition in thermal stability between

the single strand- and the collective cable regime, which is reported in NbTi cables and sub-sized

Nb ₃ Sn cables, is not clearly seen in the magnetic field dependence of this full-sized cable and

only a weak transition is found in its current dependence.

Acknowledgements

This report concludes my work performed on the DS cable and with which the final part of the master program of the study Applied Physics at the University of Twente is finished. I have learned a lot during this last year, not only about being a researcher, but also practical experience and skills gathered in the lab and workshop. I had a very nice time at the EMS chair at the University of Twente and I like to thank everyone of the EMS chair for the pleasant work environment.

I want to thank Herman ten Kate and Marc Dhall´ e for the opportunity to do my master assignment within the research chair EMS and to perform research on this great project. I enjoyed working on this experiment and with this unique set-up. I am satisfied with the results, especially because a poster of this research was presented at the Applied Superconductivity Conference 2012 and a journal paper will be written.

I specifically want to thank my supervisor Marc Dhall´ e for all the discussion and meetings we had. Those discussions contributed a lot to the final result. I also thank him for correcting this report in the evenings and during night, so it could be finished on time.

The lab can not be operated without its lab engineers, who make everything possible in the lab. Specifically I would like to thank Sander Wessel for all the work he helped me with in the project and all the practical skills I learned from him. I also like to thanks to the rest of the people in the lab for their help when needed.

The PhD student Michiel de Rapper performed similar measurements at the FRESCA test facility at CERN. During his fourth year of his PhD, he helped me a lot with my experiments.

I like to thank Michiel for his help, the discussions we had and for sharing his knowledge about

these type of measurements.

Contents

1 Introduction 5

1.1 Superconductivity . . . . 5

1.2 LHC upgrade . . . . 10

1.2.1 CERN . . . . 10

1.2.2 DS Magnet . . . . 11

1.3 Overview report . . . . 13

2 Experimental Details 15 2.1 Sample Description . . . . 16

2.2 Sample Preparation . . . . 17

2.2.1 Sample Holder . . . . 17

2.2.2 Heat Treatment . . . . 21

2.2.3 Impregnation . . . . 22

2.3 Measurement Setup . . . . 25

2.3.1 Superconducting Transformer . . . . 25

2.3.2 Cryogenic Press . . . . 29

2.3.3 Minimum Quench Energy Setup . . . . 32

2.4 Experimental Protocol . . . . 34

2.4.1 Critical Current . . . . 34

2.4.2 Transversal Stress . . . . 36

2.4.3 Minimum Quench Energy . . . . 36

2.5 Correction factors & Mechanical consideration . . . . 37

2.5.1 Magnetic Self Field Correction . . . . 37

2.5.2 Mechanical Considerations . . . . 38

3 Results 40 3.1 Magnetic field dependence of the critical current . . . . 40

3.2 Transverse stress dependence of the critical current . . . . 43

3.3 Thermal stability . . . . 47

3.3.1 Field dependence . . . . 47

3.3.2 Current dependence . . . . 48

4 Discussion 49 4.1 Magnetic field dependence on the critical current . . . . 49

4.2 Transverse stress dependence on the critical current . . . . 52

4.3 Thermal Stability . . . . 53

5 Conclusion & Recommendation 57

5.1 Conclusion . . . . 57

5.2 Recommendations . . . . 58

Bibliography 59 Appendices 62 A Preparation of Nb 3 Sn Rutherford Cables on the U-shaped holder 63 A.1 Heat Treatment . . . . 64

A.2 Mounting the sample to the sample holder . . . . 65

A.3 Impregnation . . . . 67

A.4 Connecting the sample to the transformer . . . . 69

A.5 MQE heater . . . . 71

A.6 Connecting the transformer to the rest of the set-up. . . . 72

B Protocol to operate the transformer 74

C Calibration Extensometer 76

D Analyzing the press with the extensometer 79

E Control Unit 81

F Scheme of new support structure 84

Chapter 1

Introduction

This report describes the results of a Master Assignment within the MSc. Program of Applied Physics at the University of Twente. The assignment was to investigate the critical current and the thermal stability of a state-of-the-art superconducting Nb 3 Sn Rutherford cable that was produced by CERN within the framework of the LHC upgrade program. CERN has requested the chair Energy, Materials and Systems (EMS) at the University of Twente to determine the magnetic field and transverse pressure dependence of the critical current of this cable in order to validate it for application in DS-type dipole magnets. At the end of these experiments, it was decided to use the same sample to determine also the thermal stability of this type of cable under application-relevant conditions. The present chapter aims to provide an introduction to the key concepts in the assignment. It starts of with a brief discussion of superconductivity in general and of Nb-based superconducting Rutherford cables in specific. It then moves on to give a concise description of the LHC upgrade program at CERN and of the role of the DS magnets, which form an important first step in this program.

1.1 Superconductivity

Accelerator and fusion magnets need to be built from superconducting cables in order to achieve high magnetic fields. Proper characterization of the superconducting properties of cables made from the best performing materials available is therefore essential to achieve higher magnetic fields. Key aspects of superconductivity relevant to the research assignment are described in this section. More general information about the fundamental aspects of superconductivity can be found in the book of Cyrot [1], while detailed considerations about superconducting magnets is discussed in the book of Wilson [2].

The Dutch physicist Heike Kamerlingh Onnes discovered superconductivity in 1911 in his laboratory in Leiden. After liquefying helium at 4.2 K he measured the temperature-dependent DC resistivity of mercury. The resistivity suddenly dropped to zero when the temperature decreased below 4.2 K. He named this phenomenon superconductivity [3].

In the normal state above the critical temperature T c , a superconducting material behaves as a normal conductor with Ohmic resistivity, while in the superconducting state below T _c the resistivity is virtually zero. However, this zero-resistance state is only maintained up to a certain current density. The relation between the current I through and the electrical field E across a superconducting sample is usually described with a highly non-linear power-law relation:

E = E _c

 I

I _c (B, T )

 n

, (1.1)

with E _c an electrical field criterion (often chosen as 10 ⁻⁵ V/m) and I _c the so-called critical current of the superconductor. The value of I _c depends on the magnetic field B and on the temperature T. The so-called n-value defines the quality of the conductor, a high n-value results in a sharp transition. For superconducting applications it is important that the n-value is high, so that at the operation current (typically a given percentage of I _c ) virtually no energy is dissipated in the conductor. In Figure 1.1 a superconductor with a n-value of 10 and one with 40 are compared. The voltage build-up in materials with the lower n-value starts much earlier.

n=10 n=40

I _c E c =1 · 10 ⁻⁵ V/m

Current [A]

E [V/m]

Figure 1.1: Electrical field as function of current for n=10 (red) and 40 (black), both with the same I _c .

Figure 1.2: The critical surface of Niobium-Titanium and Niobium-3-Tin.

The temperature and magnetic field dependence of the critical current are represented by the so-called critical surface which, for typical NbTi and Nb 3 Sn conductors, is shown in Figure 1.2.

For each current value above the critical surface, the superconductor is in the normal state while

below the surface it is superconducting. NbTi and Nb ₃ Sn are the two superconducting materials that are still mostly used for large scale superconducting applications. NbTi is a ductile material and is easy to work with, but is limited by a relative low-lying critical surface. Nevertheless, because of the robustness of the material, most magnets built in the past are made from NbTi.

However, it can be seen in Figure 1.2 that the critical surface of Nb ₃ Sn is higher-lying than that of NbTi and thus Nb 3 Sn is a material from which more powerful magnets can be built. For applications that require a higher magnetic field, one has to choose for the brittle Nb ₃ Sn. Apart from some niche-applications (mainly power cables, cryogenic current leads and some relatively low field magnets), the newer practical superconducting materials (MgB 2 , Bi 2 Sr 2 CaCu 2 O 8 and YBa ₂ Cu ₃ O ₇ ) are for technical and/or commercial reasons presently deemed to be not yet ready for large scale superconducting applications.

Superconducting wires cannot be made from a monolithic piece of superconductor. Nb 3 Sn needs to be embedded in a normal metal matrix for mechanical and thermal stability reasons.

For sufficient stability and low AC loss, a Nb 3 Sn wire needs a substructure of fine filaments typically (50 µm in diameter) which must be twisted. Presently, three distinct wire fabrication techniques are used to produce commercial Nb ₃ Sn wires: the bronze process, the Internal Tin process and the Powder-in-Tube process. The typical wire cross-sections that result are shown in Figure 1.3. For all methods it is important that there is a pure copper part in the wire with a high thermal conductivity and a low electrical resistivity.

Figure 1.3: Schematic presentation of the three main Nb ₃ Sn wire fabrication techniques. From top to bottom: The bronze process, the Internal Tin process and the Powder-in-Tube (PIT).

The compositions indicated are prior to the heat treatment that converts the Nb and Sn into Nb ₃ Sn. To the right SEM cross-sections are shown from actual wires fabricated according to these production methods [4].

The bronze process was the first viable wire fabrication process. Niobium rods are inserted

in a high-Sn bronze matrix and surrounded by a pure copper sheath for stabilization. A barrier

surrounds the bronze to prevent Sn from diffusing into the pure copper. Typically, large starting

billets (with diameter of several tens of cm) are first extruded and then drawn to the final wire diameter (typically below 1 mm). The bronze route is a well-established and still widely used technology, but the maximum non-copper current density obtained in this type of wires achieved is about 1000 A/mm ² at 12 T and 4.2 K [4]. This value is limited by the relatively slow diffusion of Sn out of the bronze and into the Nb, which leads to undesired Sn gradients inside the final Nb 3 Sn filament and sometimes even to incomplete reaction. For this reason, two new processes were developed, aimed at a more mobile Sn distribution.

The Internal Tin process is based on tin cores surrounded by Niobium rods, which are in turn embedded in copper. For the Restack Rod Process (RRP), these rods are extruded to a length of several meters. A diffusion barrier of Ta or Nb is wrapped around them and several of these rods are re-stacked in a pure copper matrix. The diffusion barrier prevents tin from diffusing into the pure copper matrix. This bundle is then extruded to fabricate a wire of several kilometers length. The maximum non-copper current density achieved with this process is about 3000 A/mm ² at 12 T and 4.2 K [4].

In the Powder-in-Tube method (PIT), hollow Nb tubes are filled with a powder of NbSn 2

and additional elements and stacked in a high purity copper matrix. The main advantages of the PIT method are the high tin mobility and reactivity, which results in a very short reaction time at relative low temperatures. As a consequence (and in contrast to the RRP process), the wires can be made with small well separated filaments of 30-50 µm. The maximum non-copper current density achieved is about 2300 A/mm ² at 12 T and 4.2 K [4].

Figure 1.4: Schematic of a Rutherford Cable.

Large magnets need to be built from superconducting cables made from several strands,

since single-strand windings schemes would lead to prohibitively large self-inductances. Several

superconducting cable designs are possible. For accelerator magnets, mostly Rutherford cables

are used. A schematic of such a Rutherford cable is shown in Figure 1.4. The cable is manufac-

tured by flattening a twisted ring of strands into a rectangular cross-section with four cylindrical

rollers. Sometimes a Rutherford cable has a small keystone which allows the cable to be stacked

more naturally around the aperture of the magnet. A keystone means that one side of the cable

is a little thinner than the other one. To ensure a homogeneous current distribution throughout

the cable, the strands need to be transposed so that each wire ’feels’ the same environment. In

practice this is done by twisting them around each other prior to the cable rolling step. The

twist pitch of a cable is the length measured along the cable between two successive equivalent

positions of a strand. The current density over the whole cable cross-section is much lower than

the non-copper current densities cited in the discussion of the fabrication processes, since in

the cable there is also copper, insulation and voids between the strands. Note that the com-

bined twisting/rolling step in the cabling process involves considerable material deformation,

especially at the cable edges where the strands are forced to bend round over a small radius of

curvature. Despite the fact that this deformation is imposed prior to the heat treatment during which the brittle Nb ₃ Sn is formed, the filamentary cross-section can be pinched off or the thin barrier layers can locally rupture, leading to a reduction of the critical current. Indeed, one of the important questions in this assignment is whether the new cabling process developed at CERN for RRP strands maintains the high current density which is achievable with this type of wires.

For magnet designers it is also important to know the thermal stability of the cable. Small disturbances (such as movement of the current-carrying cable in a background magnetic field, flux jumps, crack formation and specifically for accelerator magnets the impact of high energetic particles) may increase the temperature locally within a single strand. If the temperature rises above the critical current, the strand locally becomes resistive and generates Joule heating. The area where the temperature is above the critical one is called the normal zone. Due to the Joule heating the normal zone grows and propagates along the strand. However, if the initial normal zone is small enough, cooling at its ends is larger than the heat generation throughout its length and the strand will recover from the local disturbance. Moreover, Rutherford cables consist of several strands and the current inside the normal zone can redistribute to neighbouring strands and so that less current flows through the normal zone, resulting in less Joule heating and thus easier recovery. If the disturbance is too large or the current cannot be redistributed, the whole cable will go to the normal state. The loss of superconductivity in the whole cable is called a quench. During a quench all energy stored in the cable or magnet will be turned into heat that will be deposited in the magnet and resistors parallel to the magnet. To prevent quenches, the smallest amount of heat needed to quench the cable needs to be known: it is called the Minimal Quench Energy (MQE).

There are three types of propagation of the normal zone. The zone propagates in the longi- tudinal direction along the strand or it can propagate in the transverse direction to neighbouring strands. The propagation in the transverse direction may occur in two ways. The first is to adjacent strands running parallel to the normal zone, while the second is cross propagation to the strands on the other side of the cable. The propagation of heat to other stands will increase their temperature and thus lowers the critical current of those strands. Adjacent propagation is the primary mode of transverse propagation.

The recovery of a strand inside a Rutherford cable depends on several parameters. The current from the strand that is in the normal state redistributes to the neighbouring strands.

If these strands can sustain the extra current, the cable can operate with one normal strand and the strand can recover. If the neighbouring strands cannot sustain the extra current and also become normal, the whole cable will quench. This later case is the so-called single strand regime (regime I) where the quench behaviour of the cable is essentially determined by the quench behaviour of a single strand. If the neighbouring strands can sustain the extra current, the cable is much more stable since also the neighbouring strands must quench. This is called the cable regime (regime II) where the quench behaviour depends on the heat propagation through the cable and whether or not more stands will quench.

The current in the neighbouring strands will increase as each takes over about half the current sent through the quenched stand. In principle the cable is thus in the cable regime for currents below 66% of the critical current. However, heat propagated to these adjacent strands reduces their critical current and thus less current can be transferred to these strands.

The current at the transition between the single strand and cable regime is called I _kink . If

the neighbouring strands also quench but their neighbouring strands can take over the current

(i.e. the next-nearest neighbours of the originally disturbed strand), the cable can sustain three

normal strands and still recover. This goes on to higher order regimes where each time two extra strand will quench [5, 6].

Willering [6] experimentally demonstrated these regimes in NbTi Rutherford Cables. These cables are not impregnated and are in good thermal contact with the helium bath. An impreg- nated cable has comparatively limited cooling power, since the superconductor is not directly in contact with the helium bath. Nevertheless De Rapper [7] proved on sub-sized LARP and SMC cables that the different stability regimes also occur in impregnated Nb ₃ Sn Rutherford cables. In this work, we had the opportunity to test these quench scenarios for the first time in a full-sized state-of-the-art Nb 3 Sn cable. Even if CERN did not commission this experiment, we deemed this opportunity too important not to attempt this extra experiment at the end of the I _c (B) and I _c (σ) measurements.

1.2 LHC upgrade

1.2.1 CERN

The European Organization for Nuclear Research (CERN) is home to the Large Hadron Collider (LHC), the biggest particle accelerator in the world. CERN is a large international collabora- tion of many nations and institutes. The LHC is a ring-shaped accelerator with a circumference of 27 km where protons are accelerated to almost the speed of light. A schematic of the LHC is shown in Figure 1.5. In two tubes protons move in opposite direction to collide at four lo- cations where the beam pipes meet. At each of the four locations, a detector (ATLAS, CMS, ALICE or LHCb) is present to measure various data from the collisions. A well-known ex- ample one of the things the ATLAS and CMS detector are looking for is the Higgs particle.

During these proton-proton collisions many sub-atomic particles are created. The maximum energy the protons have at the moment of a collision is 4 TeV, so an energy of 8 TeV per colli- sion. The LHC is designed to accelerate the protons to an energy of 7 TeV and thus a collision energy of 14 TeV, but that will be achieved after the shut-down of 20 months at the end of 2012.

Figure 1.5: Schematic of the Large Hadron Collider at CERN.

Scientists are looking for rare particles created during the collisions, so that many collisions are needed. To achieve this, there will be 2808 bunches in each beam pipe with 1.15 · 10 ¹¹ protons per bunch once the LHC operate at full capacity. The luminosity L is the number of particles passing down the line per unit time, per unit area. The maximum luminosity achieved by the ATLAS experiment at this moment is 7.73 · 10 ³³ cm ⁻² s ⁻¹ with a collision energy of 8 TeV [8]. More information about particle physics can be found in the book of Griffiths [9].

The ring of the LHC contains 1232 dipole magnets of 15 m length and 392 quadrupole magnets of 5-7 m long. The dipole magnet keeps the beam on a circular trajectory by generating a magnetic field of 8.33 T perpendicular to the particles and thus bending the beam by the Lorentz force. The quadrupole magnets are used to squeeze the beam together in order to keep it focused.

The proton bundles are not perfectly focused in the center of the beam pipe. A small part will move out and hit the superconducting magnet and release a small amount of energy. If too many particles hit the superconducting windings of the magnets, a quench will occur. Collima- tors are used to clean the proton bundles and thus reduce the number of particles colliding with the superconducting magnets and to prevent a quench. However, the present collimators do limit the maximum beam intensity. The second phase of the LHC collimation upgrade consists of installing two additional collimators in the dispersion suppressor (DS) region of points 2, 3 and 7 of the LHC and will enables proton and ion beam operation at nominal and ultimate intensities.

The LHC is entirely constructed with NbTi magnets, which at the time of its conception were conceived as the more robust technology. Meanwhile, plans are made for a luminosity - and, in a later stage, energy upgrade of the machine. This will require higher magnetic fields, initially in the quadrupoles that focus the beams just before the experiments (luminosity upgrade) and later in the bending dipoles along the entire tunnel (energy upgrade). Since NbTi is intrinsically limited to fields of about 10 T (Figure 1.2), these magnets will need to be Nb ₃ Sn-based. As a first step in this process, aimed at gaining experience with Nb 3 Sn magnets constructed with the newer PIT and RRP high-current strands, a number of Nb 3 Sn DS magnets will be installed to achieve the collimation upgrade discussed above. The cable investigated in this assignment is designed to be used in these magnets.

1.2.2 DS Magnet

The necessary longitudinal space of about 3.5 m for the additional collimators is provided by replacing some of the 15 m long 8.33 T NbTi dipole magnets by a pair of 5.5 m long 11 T Nb 3 Sn magnets. The new magnets are placed in the DS region and are therefore called DS Magnets.

They are connected in series with the rest of the ring and are therefore operated at a current of 11850 A at 1.9 K with 20% operation margin [10]. The degradation of the critical current due to cabling has to be 10% or less to provide the required operation margin [11]. These magnets are straight instead of having the shape of the curvature of the ring, which means that a wider coil aperture is needed (60 mm). A cross-section of the DS magnet is shown in Figure 1.6. This design results in a homogeneous magnetic field in the center of the magnet.

The stress distribution in the DS magnet is simulated by Karppinen et al. [10]. Two designs

are simulated, one with a removable pole and the second with an integrated pole. The azimuthal

stress distribution of both designs is shown in Figure 1.7 for room temperature, after cool-down

and at 12 T generated field. The maximum coil stress is below 145 MPa for the removable

pole and below 150 MPa for the integrated pole. The maximum coil stress occurs transverse to

the cable, on the midplane of the magnet as can be seen from Figure 1.7. Just like with other

superconductors, the properties of Nb ₃ Sn changes when the material is mechanically loaded.

Figure 1.6: DS magnet cross-section with geometrical field errors

For relatively low strain levels (below the so-called irreversible strain limit), deformation of the crystal lattice changes both the electronic band structure of the material and its phonon spectrum. This leads to a gradual ’shrinking’ of the critical surface, i.e. a reduction of I _c [12].

However, as soon as the strain is released, the original properties are recovered. At higher

strain, the composite wires yield and the brittle Nb 3 Sn filaments start to crack. The resulting

I _c reduction is not recovered when the strain is released and hence it is called irreversible. Since

the magnet will be ramped up and down often, it is essential that the degradation due to the

operational transverse stress is reversible. It is therefore important that the margin on the cable

is such that it will not reach the irreversible degradation regime, thus preventing damage to

the cable. As will be described in the following chapter, the University of Twente developed a

unique facility to test the I c sensitivity to the transverse stress in Rutherford cables continuously

and in situ. At CERN and other accelerator labs around the world, this important property can

also be measured, but there it requires pre-stressing of the cable prior to cool-down so that a

full I c (σ) characterization involves a cumbersome and complicating sequence of cool-down and

warm-up cycles. Therefore, CERN asked the University of Twente to test their DS cable also

under transverse stress.

Figure 1.7: Azimuthal stress distribution in the coils after the cold mass assembly at room temperature (top), after cool-down (middle) and at 12 T (bottom) for removable (left) and integrated pole (right) designs.

1.3 Overview report

The first goal of this assignment was thus to measure the field and transverse stress dependence of the Rutherford cable that will be used in the DS magnet. The second goal was to measure the thermal stability of this cable. Both goals have been achieved and the results are included in this report. In this section a summary of the work performed and the outline of the report is given.

The experimental setup had not been used on full-size cables for many years and since then the critical current and properties of Rutherford cables have changed a lot. Present cables have a much higher critical current density compared to the cables measured previously on this set-up. In the course of the LHC upgrade program, it is foreseen that several different cables will be measured at the University of Twente for CERN. At the start of this experiment, it was expected that the first cable to be measured was the so-called FRESCA II cable, which is needed for the upgrade of the FRESCA test facility for superconducting cables at CERN. This cable has strands of 1 mm diameter resulting in a big and relative stiff cable. To test whether this cable could be bent around the sample holder without internal damage, experiments were performed to validate the sample holder, by searching for damaged filaments in the cross-section. The sample holder itself and the results of this initial micro-structural characterization experiment are discussed in Section 2.2.1.

The DS and FRESCA II cables have a much higher current density compared to samples

measured previously on this set-up, which results to much higher currents and therefore higher

Lorentz forces. Simulations were performed to determine the Lorentz forces and the self field

of the FRESCA II cable and of the DS cable. These calculations are described in Section 2.5.

CERN eventually decided that it was more important that the DS cable was measured first, so that the rest of the research in this assignment was performed on this cable. The FRESCA II cable will be measured in the future and is no further part of the master assignment. Before measurements could be performed, the setup had to be modified and the control unit repaired.

A vacuum chamber and attributes for impregnation had to be constructed and a new support structure for the MQE measurements had to be designed. The experimental details are found in Chapter 2. The sample preparation is found in Section 2.2. The measurement setup of the transformer, the press and the MQE measurements are described in Section 2.3. The measure- ments are performed following the protocols described in Section 2.4.

Three samples from the same batch of the DS cable were measured. The first two were not successful since the samples became damaged during the measurements. The first sample was damaged due to the Lorentz forces of the selffield of the cable (see §2.2.1). Press measurements were nevertheless performed on the first sample to test the press set-up. The second sample was damaged because the impregnation was unsuccessful, as was found during the experiments (see

§2.2.3). However, from these two sample a lot was learned and the preparation procedure was modified to prevent future problems. The modifications to the sample preparation procedure, set-up and experimental procedure due to the first two sample on the set-up are discussed in the relevant sections in Chapter 2.

The third DS cable sample was successfully measured with respect to the critical current as function of the peakfield and transverse stress, as described in Sections 3.1 and 3.2 respectively.

During the first experimental run the press measurements went wrong due to a short circuit

over the magnets that energize the press, but the cable sample was not damaged. The problem

with the press was fixed, but the setup had to be warmed up to room temperature. Then the

critical current was measured at applied fields of 10, 10.5 and 11 T and press measurements

were performed with transversal stresses up to 270 MPa. Since the cable was only degraded

2% irreversibly, it was decided that this sample could also be used for the MQE measure-

ments, the results of which are found in Section 3.3. All results for sample 3 are discussed and

compared with other measurements in Chapter 4. The conclusions of the measurements are

found in Chapter 5.1. Recommendations for future measurements with this set-up are found in

Section 5.2.

Chapter 2

Experimental Details

Measuring the critical current in long samples of full-sized Rutherford cables under application- relevant conditions requires a considerable infrastructure in terms of current, and, especially, magnetic field. In order to apply a uniform magnetic field over a straight ∼1 m long cable sample, a wide-bore dipole magnet is needed. When materials become better-performing (as described for Nb ₃ Sn in the previous chapter), one is faced with the general problem that existing test facilities, constructed with ’older’ technology, are stretched to their limits when called upon to investigate ’newer’ technology.

A typical example of this dilemma is the FRESCA facility at CERN, which was constructed with a 1.9 K NbTi 10 T magnet for the investigation and quality control of the NbTi cables used in the LHC magnets [13]. Since the LHC upgrade requires Nb 3 Sn magnets operating above 10 T, FRESCA results need to be extrapolated to higher field in order to gauge the behavior of the modern Nb 3 Sn cable now under development. Indeed, this is exactly the motivation behind the FRESCA II project mentioned before, which seeks to replace the NbTi dipole with a more modern Nb ₃ Sn one [14]. This explains why not many long-sample experiments are performed on Rutherford cables world-wide.

In order to circumvent this problem, short-sample experiments were designed and realized at the University of Twente already in the run-up to the late eighties and early nineties. A transformer-powered [15] U-shaped cable sample can be fitted in the bore of a relatively simple solenoidal labmagnet, eliminating the need for a high-current power supply and a large-scale high-field dipole. A compact but powerful electro-magnetic press [16] furthermore allows to test the cable samples under magnet-relevant transverse pressure levels.

Even if this infrastructure was constructed many years ago, some of it had not been used for

a long period and needed revision, while all of it needed modifications in order to accommodate

the present Nb ₃ Sn cables. The short-sample MQE experiments is new and the instrumentation

for these measurements needed to be designed and realized. This chapter describes all these

experimental aspects. Section 2.2 gives a description of the investigated cable, while Section 2.2

explains how samples of it are prepared and mounted in the set-up. The measurement set-

up itself is described in Section 2.3. The measurements are performed following the protocol

described in Section 2.4. Finally, necessary self field corrections and mechanical considerations

are found in Section 2.5.

2.1 Sample Description

The DS cable is a Rutherford cable of 40 strands with a keystone of 0.75°, cabled at CERN.

The strands are 0.7 mm in diameter and are manufactured by the RRP process by Oxford Superconducting Technology (OST) with a strand configuration of 108/127. This means that 108 of the 127 rods are Nb 3 Sn and the center 19 rods are pure copper rods. The cable is optimized for achieving both mechanical stability and minimal damage to the delicate internal configuration of the strands. Figure 2.1 shows a cross-section of the DS strand and of the DS cable. Also a top view of the cable is shown. Tables 2.1 and 2.2 present the key parameters of the strand and cable, respectively.

Figure 2.1: The cross-section of the DS strand (top left) and of the DS cable (bottom) as well a top view of the DS cable (top right) [17].

Table 2.1: DS Strand Parameters, RRR is the ’residual resistance ratio’, the ratio between the normal-state resis- tance of the strand at room- and cryogenic temperature.

The other parameters are discussed in Section 1.1.

Parameters Value

Manufacturer OST

Design RRP-108/127

Strand diameter 0.700±0.003 mm

Cu fraction 53±3 %

Effective sub-element diameter <60 µm Critical current I _c (12T, 4.2K) >475 A Critical current density J c (12T, 4.2K) >2650 A/mm ² RRR (after heat treatment) >60

Twist pitch 14±2 mm

Table 2.2: DS Cable Parameters, the parameters are discussed in Section 1.1.

Parameters Value

Manufacturer CERN

Number of strands 40

Width 14.7 mm

Height 1.25 mm

Keystone 0.75°

Twist Pitch 100 mm

2.2 Sample Preparation

2.2.1 Sample Holder

The sample (1) is mounted on a stainless steel U-shaped sample holder (2) as shown in Fig- ure 2.2. The 46 mm long flat ’bottom’ of the U-shaped sample holder is in the middle of the high field area of the solenoidal lab-magnet. The 90 ° bends of the U-shaped holder have a radius of 10 mm. The cable is impregnated on the sample holder (see §2.2.3) and is kept in place by epoxy clamps (3) on the straight ’legs’ of the U and by two lateral support plates (4) in the high field area. The ends of the sample are soldered to the secondary loop (5) of the transformer (6) with a resistance of typically 1 n W (see §2.3.1). The cable is fixed along these joints by Stycast clamps (7). The epoxy and Stycast clamps protect the cable against the electromechanical forces generated by the magnetic field. The sample holder is fixed to the magnet by the halve circles (8) attached to the sample holder. It was found during the initial experiments that this fixation of the sample is required because the main magnet quenched after a sample quench at an applied transversal pressure of 20 MPa. The exact reason for these magnet quenches remains unclear, but fixing the sample holder to the magnet solved this problem.

8 B B B B B B M 7

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Figure 2.2: The second sample (1) fully mounted on the U-shaped sample holder (2). The cable is fixed in place by epoxy clamps (3) and lateral support plates (4). The joint (5) connects the sample to the transformer (6) en is fixed to the sample holder by Stycast clamps (7). The halve circles (8) fixed the magnet to the sample holder.

All samples show some training quenches before the cable finally reaches its ’true’ critical current (i.e. the current level at which a gradual and reproducible voltage build-up is observed instead of a sudden thermal runaway) and is ready for measurements. This well-known trainings phenomenon is caused by energy releases due to Lorentz-force driven movement of the cable or individual strands in the applied magnetic field, which results in inductive voltages. As the sample gradually ’settles’ against it supports, its performance will gradually increase over the training quenches, until the cable reaches its final position. The training behavior depends on the preparation quality of the sample. During the training of the cable the quench current I q

is measured by reading out the shunt resistance ( §2.3.1). The normalized quench current of

the three samples is shown in Figure 2.3. Sample 1 and 3 have a layer of polyimide tape of

Figure 2.3: The current levels at which the training quenches of the three samples occured, normalized to the critical current of sample 3.

25 µm between the sample and the sample holder, while sample 2 was partially bonded to the sample holder. The difference is clearly seen in the number of training quenches required before I _c measurements can be performed.

The decrease in quench current of sample 1 after the eighth quench is where this sample

’bulged out’ under influence of its self-field, as discussed in Section 2.2.3. Sample 2 increased slowly until I _q /I _c value of 0.85-0.90 after which the quench current fluctuates a lot. These fluc- tuations clearly indicate that the cable does not quench because it exceeds its critical current, but due to random disturbances such as movement of or crack formation in the cable/epoxy sample pack. These might be caused by the ill-defined bonding with the sample holder, which results in local stress build-up caused by the differential thermal contraction between the sample holder and the sample.

Sample 1 became damaged, but nevertheless a critical current could still be determined.

The training quench currents before the sample was damaged at 10 T applied magnetic field and after the damage at 11 T applied magnetic field and the critical current afterwards (at 10.5 and 11 T applied magnetic field) are shown in Figure 2.4. It can be seen how the sample reached the expected critical current (i.e. 40 times the critical current measured on a virgin witness strand, see §2.2.2) during the training quenches. However, after quench number 7 the cable was significantly degraded.

From these observations on sample 1 valuable lessons were learned with respect to the fixa-

tion of the long current leads (the legs of the U) against the sizeable Lorentz forces, as will be

discussed further in Section 2.2.3. At the beginning of the assignment, when the FRESCA II

cable was still expected to be the main focus of the experiments, some preliminary tests were

performed on the possible influence of sample deformation around the U-shaped holder. The

Figure 2.4: The quench currents of sample 1 (black circles) for the training quenches before the cable became damaged at 10 T applied field and quench currents at 11 T after the damage.

The blue squares are the measured critical currents. All data are at T=4.2 K.

sample is bent around the corners of the sample holder, which results in compressive strain on the inside of the cable and tensile strain on the outside. This might cause filaments to break.

If the strands are damaged in the bending process, the current will redistribute to undamaged strands, causing some strands to carry more current than others and thus influencing the critical current measurements. It is therefore imperative that the cable is not damaged by the bending process.

The Fresca II cable has a cross-sectional area of 21x1.8 mm ² and is wound from 40 strands of 1 mm diameter. This is a large and stiff cable, which might give problems during preparation.

The Fresca II sample will be tested on transverse stress and therefore the question was whether

the sample can be bent around a bending radius of 10 to 20 mm so that 46 to 26 mm long

straight section remains available in the high field area for transverse pressure tests. To test

this, the cable is bent, partially reacted and cross-sectional cuts are made and polished to be

examined under a microscope for broken filaments. Broken filaments in PIT wires are known to

result in copper diffusing into the strand and tin diffusing to the copper matrix. This will result

in the formation of bronze in the filaments and the copper matrix. The bronze is found by the

color difference compared to the niobium or copper. Since the fabrication of a new stainless

steel holder is costly and the optimal dimensions are not yet certain, a wooden mock-up of the

holder is made with a bending radius of approximately 20 mm. It is known that the elastic

part of the deformation of the wire does not damage the filaments. The plastic part of the

deformation, on the other hand, can result in broken filaments. To find broken filaments by tin

leakage, only the plastic part of the deformation is required. Therefore, the sample could be

taken off the mock-up mold and put in the oven without support. A quick reaction program

of 12 hours at 650 °C, with a ramping speed of 50 °C/h, is given to the sample. In this time possible diffusion of the copper and tin is already visible if present [18]. The cable is now only partially reacted, but the possible diffusion already occurred, so a full reaction process is not necessary.

Cross-sectional cuts are made in both bends (the corners of the U), the straight part of the high field area (the bottom of the U) and of the current lead (the legs of the U). The current lead is not bent and all damage found in this part is due to the cabling process and not to the deformation of the sample on the holder. To fix all strands during polishing, the cable is fully soldered before the pieces of the cross-section are cut and then embedded in Stycast 2057 under vacuum. The cross-sections are abraded and polished to achieve a micrometer resolution with the microscope.

Figure 2.5: Cross-section at the unbent part of the current of the edge of Fresca II cable. The damage to the filaments (seen by the bronze in the filaments), due to the cabling process, is marked with the red circles.

The strands at the side of the cable have many broken filaments, since at this location they are strongly deformed during the cabling process. Damage and deformation at the edge of the unbent part of the current lead is shown in Figure 2.5. The damage that shows up as bronze between and in the filaments is the same over all cross-sections that have a single strand at the edge. The rest of the strands (i.e. those not at the edge of the cable) sporadically have a broken filament, but only a few are found as shown in Figure 2.6 with one bronze filament. The filaments are a little deformed in the bending, but this did not cause broken strands.

The conclusion of the analysis of these cross-sections is that the Fresca II cable can be

wound on a U-shape sample holder with a bending radius of 20 mm or larger without broken

filaments. In the future, same experiment will have to be performed on a reaction holder with

a well defined bending radius of exactly 10 mm. Since no damage at all is found after 20 mm

Figure 2.6: Cross-section of a strand at the middle of the high field area of the center of the Fresca II cable. This is one of the few strands in the cross-sections that has a bronze filament (red circle).

bending, the bending radius can be made smaller. During this assignment, the 10 mm bending radius test is not performed because the measurements on the DS-cable had a higher priority.

No further reference to the FRESCA II cable is therefore made in the remainder of this report.

2.2.2 Heat Treatment

Nb ₃ Sn is a brittle material and therefore strands, cables or even entire magnets have to be wound of bent into their desired shape before the heat treatment, when the Nb and Sn is still unreacted and the material is ductile. The cable is reacted on a reaction holder and after the heat treatment mounted on the sample holder. The clamps and supports of the reaction holder keep the cable in the desired shape during the heat treatment, when the Cu is soft and might flow otherwise. Before mounting the sample on to the reaction holder, it is wrapped in two layers of 0.15 mm thick glass fiber matting, which prevents the sample from sticking to the holder.

A virgin witness strand is wound on a standard ITER barrel, shown in Figure 2.7, to be

reacted together with the sample. A ’virgin strand’ is the term for a strand from the same

batch as wires with which the cable was made, but with which nothing happened. This witness

strand is used for comparison with the cable sample. Due to the large deformation involved in

the cabling process (Figure 2.5), Rutherford cables may suffer a reduction in critical current

compared to un-deformed wires and such degradation of the cable can be gauged by compar-

ing the I _c -value of the cable to that of the witness strand. The witness strand will allow to

predict the ’ideal’ value of the critical current for an undamaged cable by multiplying the I c of

the witness strand with the number of strands. The witness strand is soldered to the current

Figure 2.7: The witness strand on the I _c barrel.

terminals (the Cu rings on either end of the cylindrical holder in Figure 2.7) and by standard I c measurements its critical current as function of magnetic field is determined.

’Extracted strands’ are taken from a piece of unreacted cable. Single strands of 15 cm long are carefully pried loose from the cable and several of them are put in between two stainless steel plates wrapped up in glass fiber matting. These strands will be used to measure the Residual Resistivity Ratio (RRR) on the thick edge, on the thin edge and in the center of the cable. The RRR value is defined as ρ 300K /ρ 20K . The RRR value gives information about quality of the strands (the Sn leakage in damaged strands discussed above leads to increased impurity scattering in the Cu matrix and hence to a lower RRR value and will also turn out to be relevant for the thermal stability of the cable.

The sample, witness strand and extracted RRR samples are reacted together in a vacuum tube oven. The heat treatment of the DS cable has three plateaus at 210, 400 and 650 °C for 48, 48 and 50 hours respectively. The heat treatment recommended by the strand manufacturer OST prescribes a third plateau of 50 hours at 665 °C, but the RRR resulting from this recipe is around 60, which is too low for stability purposes. Therefore it was recommended to use 650 °C for the third plateau to reach higher RRR values [19].

2.2.3 Impregnation

Nb 3 Sn Rutherford cables need to be impregnated to prevent conductor movement and to protect the cable against electro-mechanical stresses applied to the cable. A press experiment on a cable that is not impregnated would result in prematurely damaged filaments and the performance of such a cable would quickly degrade, since the stress in bare Rutherford cables is concentrated at the points where the strands cross each other and can locally reach much higher levels than the overall pressure exerted on the cable. In the case of an impregnated cable the stress is transmitted through the filling material, resulting in a more uniform stress distribution [20].

As seen in Figure 2.2, part of the sample (the bottom of the U and about 1/3 of the legs) is

wrapped in glass fiber and two extra layers of glass fiber are added on top of the cable. These

2 extra layers of glass fiber are added to achieve a more hydrostatic stress distribution in the

cable. The glass fiber is drawn full with epoxy and hardened in a vacuum oven. The result is

a strong layer that forms around the cable to protect it from the forces that will be applied

during handling and during the experiment. The Lorentz force due to the combined applied

and self-magnetic field must be absorbed by the epoxy. Furthermore, the thermal stability of

the cable is also increased since the cable cannot move.

The first and third sample were not bonded to the sample holder. A 25 µm thick polyimide foil was inserted between the impregnated cable and the sample holder. The foil does not stick to epoxy, so the cable can move on the sample holder. It is kept in place by the clamps during the impregnation around the cable and by an anvil and support flanges in the high field area.

The second sample did not have polyimide foil between the cable and the sample holder and was therefore partially bonded to the sample holder. Since the stainless steel sample holder shrinks less than the cable when cooled, thermal stresses build up. After removing the second sample from the sample holder it could be clearly seen that the cable was only bonded at a few places, which furthermore resulted in local stress concentrations. As a result, the second sample required a lot of training quenches, while the samples with polyimide foil needed only four to seven training quenches as shown in Figure 2.3.

The sample is transferred from the reaction holder to the sample holder. Voltage pairs are connected to the cable, each time spanning a given length on a single strand and the glass fiber clamps on the legs of the U are made. A flat surface on the bottom part of the U between the support plates is ensured by gently pushing the sample against the holder with a Teflon block.

Impregnation is performed by lowering the sample holder with cable slowly and under a small angle in a rectangular recipient of epoxy. This is performed in a vacuum chamber in order to remove all bubbles from the epoxy. After venting the vacuum chamber, any bubbles that remain in the epoxy will shrink under normal pressure and become very small, further drawing epoxy in the glass fiber. Afterwards the epoxy is hardened in an oven. All details of the impregnation can be found in the impregnation protocol included in this report as Appendix A.3.

The impregnation process changed somewhat from sample to sample. The first sample was impregnated adequately, but after one of the quenches during the measurement the cable be- came damaged on the current lead, due to the electromechanical forces generated by the self field. In Figure 2.8a the damage is shown from the top side. The epoxy cracked open and the the cable was bent outwards. The bending of the cable is even more clearly visible in a side view as shown in Figure 2.8b. The epoxy is locally removed to examine the cable further and the bending is also clearly seen on the un-covered cable. Bending occurred only to the strands at outside of the cable, while those on the inside remained unbent. To prevent this

’bulging out’ of the cable in future measurements, the clamps are made wider. The distance between clamp two and three is too large and in the new design the third clamp is made bigger.

Also the thickness of the clamps is increased by increasing the width of the anchoring slits in the stainless sample holder. The result is a cable which is better supported with stronger clamps.

For the first two samples, the temperature of the sample holder was regulated. Whereas the first sample was impregnated well, the second one showed many bubbles in the epoxy. During the start of the impregnation there were some issues which needed unforeseen attention and meanwhile the epoxy cooled down to much. The feedback loop of the heaters on the sample holder was not fast and powerful enough to warm it up again. Since the temperature was too low, the viscosity went up and the epoxy could not be drawn in all cracks. Furthermore, a lot of bubbles stayed in the epoxy since the viscosity was too high for them to move out the epoxy.

The inside of the first impregnated cable is shown in Figure 2.9a. It can be seen that there

are only a few bubbles between the strands. The impregnation was performed well. The inside

of the second cable is shown in Figure 2.9b. There are a lot of bubbles in the epoxy. Between

the strands are series of interconnected bubbles (1). Along the edge of the glass fiber, bubbles

and pores are found on the surface (2). Finally, large pores are observed between the cable and

the lateral support plates. If the viscosity of the epoxy was too low, the bubbles cannot get out

of the epoxy and the gas voids are not pumped. When the pressure in the vacuum chamber is increased to standard pressure, the epoxy is pushed in the holes as the bubbles shrink. This happens in the direction where the epoxy flows and any bubbles remaining will form along the cable (3).

(a) front

(b) side

Figure 2.8: The damage to DS cable 1.

(a) (b)

Figure 2.9: a) Adequate impregnation and b) poor impregnation as visible in pictures from the inside of the cable, where (1) are the interconnected bubbles between the strands, (2) the bubbles at the edges of the glass fiber and (3) the bubbles stretched in the direction of the cable.

The strand diameter is 0.7 mm.

No ’proper’ critical current (with gradual and reproducible voltage build-up) could be deter-

mined of the second sample due to disturbances. By increasing the transverse stress to 20 MPa,

the cable might be better fixated. However, the measurement of sample 2 at a transverse stress

of 20 MPa resulted in a degradation of 17-23% of the quench current. It may be assumed that this degradation is caused by the bad impregnation in combination with the local bonding of the sample to the sample holder.

The problem with the impregnation is fixed by adding a second temperature control to the bucket filled with epoxy. Heaters are placed on both sides of the recipient with an extra temperature sensor. Now both the recipient and the sample holder have an individual feedback loop to regulate the temperature. This improved control allows the temperature of the epoxy to be kept constant within a few degrees. This resulted in a proper impregnation for the third sample.

2.3 Measurement Setup

2.3.1 Superconducting Transformer

A superconducting transformer is used to power the cable samples to currents up to 50 kA.

The transformer is designed and built at the University of Twente [15] and there are only a few superconducting transformers in the world. The benefits of a superconducting transformer compared to a conventional power supply are:

ˆ The transformer is considerably less costly.

ˆ A conventional power supply needs sizeable copper current leads from room temperature to 4.2 K. Helium consumption will very high due to the large thermal leak and to Joule heating in the current lead. The high-current secondary of superconducting transformer is already fully submerged in liquid helium, while the primary needs only to be powered by a room-temperature power supply of 50 A. The helium consumption of the transformer is therefore negligible compared to a conventional supply.

ˆ The superconducting transformer is small and fits above the magnet in the cryostat. The required room-temperature instrumentation next to the cryostat is small compared to the large conventional supplies.

All the components of the superconducting transformer are shown in Figure 2.10. The trans- former consists of a multi-turn primary coil (1) with around it 1.5 turns of the secondary coil (2).

Both primary and secondary coils are superconducting and made from NbTi. The secondary coil is soldered to the sample. The primary is connected to the current leads going out of the cryostat to an external power supply. Normal conducting transformers are fully resistive and have a step-response that decays directly. Therefore they can only be operated at AC current.

Since the transformer used in the experiment is superconducting, the only resistance lies in the current leads to the power supply in the primary loop and the joint resistance of the connections to the superconducting sample in the secondary. In the ideal case this joint resistance can be neglected and the current induced in the secondary by a step change of the current in the pri- mary will flow forever. In practice, there is a joint resistance of typically 1 n W and the secondary current will eventually decay. With a joint resistance of ∼1 n W and a self inductance of 0.8 µH, the decay time constant of the transformer is about 800 s. Therefore to perform measurements at a stationary current level or to ramp the current at a constant speed, a feedback loop is re- quired that increases the primary current such that the secondary current is at the desired level.

The simplified electrical scheme illustrating the essential principle of the feedback loop is

shown in Figure 2.11. A more detailed scheme including the modifications that needed to be

made to the electronics is discussed in Appendix E. Both for the experiment itself and the proper

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Figure 2.10: The components of the superconducting transformer: (1) the primary coil, (2) the secondary coil, (3) Rogowski coil, (4) Superconducting Shield of Lead-Bismuth with a Hall- sensor in the center, (5) Correction Coil, (6) Calibration Coil, (7) Heater of secondary coil (8) Heater of integrator circuit, (9) Sample Holder and (10) Joint with the sample.

operation of the feedback loop, the current through the sample must be measured accurately.

A shunt resistance is not an option, because currents up to 50 kA will cause too much Joule heating and the decay of the current in the secondary circuit will be too fast. Therefore a Rogowski pick-up coil is used to measure the current through the sample. The superconducting Rogowski coil is connected in series with a second superconducting coil with a Hall element.

The second coil and the Hall element are placed within a superconducting lead-bismuth shield to eliminate any influence of the stray field of the main magnet on the Hall probe(4). The voltage over the Rogowski coil is given by

V rog = M δI s

δt , (2.1)

where I _c is the current through the secondary coil, t is the time and M is the mutual inductance between the Rogowski coil and the secondary of the transformer. The induced current in the superconducting circuit is then given by

I cir = R V _rog dt

L _r + L _h , (2.2)

where L _r is the self-inductance of the Rogowski and L _h is the inductance of the coil at the Hall-sensor. Combining Equation 2.1 with 2.2, one sees that I _cir , which is measured directly by the Hall-sensor, is in principle always proportional to I s . In practice, there is an extra motivation. The high-sensitivity Hall probe has a limited dynamic range and therefore the current in the pick-up circuit is compensated back to zero. To achieve such a null-measurement, the signal from the Hall sensor drives a voltage-controlled current supply that powers an extra compensation coil (5) which is coupled to the Rogowski coil and cancels out the current in the pick-up circuit induced by the current (changes) in the secondary circuit. The current needed for the compensation coil is given by

I comp = I s

N (2.3)

Figure 2.11: Schematic of the feedback loop of the superconducting transformer.

where N is the number of turns in the compensation coil. This way the pick-up circuit can be made very sensitive and this time the current through the compensation coil is proportional to the secondary current. By connecting a shunt resistance in series with the compensation coil, the current through the compensation coil can be measured and thus the secondary current can be measured. In the setup a 10 m W shunt resistance is used, resulting in a ratio between the shunt voltage and the secondary current of 1 mV/kA. This voltage is used in combination with the ’set’ current to regulate the current in the primary coil. The decay due the joint resistance is in the secondary circuit compensated by this feedback-loop by gradually increasing the primary current, so that the current in the secondary coil stays constant with a fluctuation less than 1 A. By slowly increasing the ’set’ voltage, the current in the sample can be ramped.

Due to the joint resistance, the current in the primary slowly rises in order to keep the current in the secondary stationary. The maximum allowed primary current is 50 A for this transformer. The measuring time is thus limited by the maximum current through the primary coil. The faster the decay in the secondary coil, the faster the current will increase in the primary coil. A low joint resistance is therefore important. Also measuring at high currents decreases the measuring time, since most of the primary current (for typical measurements on the DS sample about 30 A) is already ’used up’ to ramp the secondary current to the desired level.

In order to achieve longer measuring times a switch is used to reverse the polarity of the primary. This would also work with a voltage-controlled bipolar power supply, but since no bipolar power supply available in the lab was compatible with the control unit, the method with the switch is used for all measurements described in this report. First the transformer is negatively powered while repeatedly quenching the secondary circuit at low negative currents.

These quenches are invoked with the aid of a heater attached to this circuit (7). Note that the

negative sample current is kept low in order to avoid ’re-training’ of the sample in the opposite

direction (see §2.2.1). This procedure is repeated until the primary current is at the desired level. Due to the forced quenches, the secondary current is zero at this point, next the primary power supply is turned off. The change in the primary current will induce a sizeable current in the secondary loop. Once the current in the primary coil is zero, its polarity can be commuted, the control of the primary supply is switched from manual to feedback mode and the feed-back loop can pick up the current. With this polarity reversal method, the primary current starts at 0 A while the secondary current is already for example at 15 to 18 kA, resulting in a much longer measuring time. A detailed manual with proper protocols for operating the superconducting transformer is included as Appendix B.

A calibration coil (6) is used to calibrate the pick-up circuit and to make an estimate of the measuring error. Heaters are added which allow to decay the current through the secondary coil (7), the pick-up circuit (8) and to heat the superconducting shield. Below the transformer different sample holders can be connected. All samples must be soldered to the transformer to ensure the low joint resistance.

A control unit which automates the feedback loop contains all amplifiers that control the power supplies. The control unit that was used in the past did not work anymore. This is fixed by replacing the feedback electronics from the control unit with a spare one that was manufactured together with the control unit for MIT [21]. The testing of the electrical unit is performed on a NbTi cable which was already on the transformer and it was verified that with the new electronics the same currents were measured on this sample as previously [22]. As an added complication, the current in the primary coil of the transformer also induces a current in the Rogowski (ideally the mutual inductance between the primary and the Rogowski should be zero. In practice it is small, but non-negligible). This undesired effect can only be par- tial compensated by the new control unit. In the calibration, an extra compensation factor of 4.73 mV/A between the primary and secondary current is measured for the new control unit to compensate for the coupling between the primary and Rogowski. The electronics are calibrated as described in Appendix E. Further details about the transformer can be found in [21, 23].

Due to the high Lorentz forces acting on the cable, the setup must be well-supported inside the magnet. A new aluminum support structure is designed that can be used for I c (B) and MQE measurements ( §2.3.3) in the 15 T magnet. This support can also be used for the big Fresca II cables. The new support structure transmits the Lorentz forces only to the flanges of the magnet and not to the magnet itself. The stainless steel anvil supporting the measurement section is kept in place by three bolts on each 2 disk springs to apply adequate stress to the sample during the cooling down and during the measurements at 4.2 K.

Figure 2.12: The sample holder with aluminum supports for MQE measurement.

2.3.2 Cryogenic Press

The cryogenic press consists of two superconducting NbTi pancake coils which are connected in series to generate a repulsive force between the coils. The press can generate a maximum force of 240 kN perpendicular to the high field area of the cable. The anvil is custom-made for the DS cable from stainless steel. The area over which the anvil presses is 45x15.2 mm ² which results in a maximum transverse stress of 350 MPa. The corners are rounded to prevent stress concentration at the corners of the anvil. On top of the anvil, there are four layers of 50 µm polyimide tape for a good contact between the anvil and the cable, resulting in a more homo- geneous stress distribution over the sample. Both the anvil as the cable have some roughness which smoothened by the polyimide tape.

A schematic of the press is shown in Figure 2.13. The two pancake coils are made from a Niobium-Titanium wire which is wet wound (with alumina-filled Stycast 2850 epoxy) around stainless steel formers. The bottom coil firmly connected to the sample holder by a thick steel cylindrical sleeve assembly which fits smugly around the holder and is attached to it with two thick fixation pins. The top coil is therefore pushed upwards when a current is passed through the press coils. A piston transmits this force to the anvil which pushes on the sample.

For the third DS sample, the press setup is modified so that the epoxy clamps can be made bigger and no epoxy has to be removed from the clamps to make it fit inside the outer sleeve that transmits the reaction force. This modification will also allow for larger samples such as the Fresca II cable to be well-supported inside the cylinder.

The force generated by the press is given by F _p = I _p ² dM ₁₂

dz ± I _p I _A dM _1A

dz − mg, (2.4)

where F p is the force generated by the press, I p the current through the press, I A the current through the background magnet, M ₁₂ the mutual induction between the press coils, M _1A the mutual induction between the upper press coil and the main magnet, m the mass of the upper press coil and the inner cylinder, g the gravitational acceleration and z 2 is the position of the upper press coil. The plus sign is when I _p and I _A are in the same direction and a minus sign for opposite direction. The correction for the main magnet depends on the field direction of the press and magnet. For the experimental configuration used in this assignment, this is determined by Verweij [24] as

F _d = I p [I p (82.47 − 2.71z 2 ) ± 0.23I _A ] − 110. (2.5) I A and I p can be determined with an accuracy < 0.1 A. The error in the force is mainly determined by the error in z ₂ and a systematical error in dM ₁₂ /dz due to imperfections in the press. The estimations for the error are ∆I _p < 0.1%, ∆I _A < 0.1%, ∆z ₂ = 0.1 mm and

∆(dM 12 /dz) = 0.2 follows ∆F p /F p < 2% [24].

The extensometer that was used in the past had to be rebuilt. A new design is made from titanium and is shown in Figure 2.14. A pin positioned on the upper press coil sticks through the cover against the extensometer. By reading out the extensometer, variations in the distance between the two coils can be monitored and the force between them can be calculated.

The extensometer is made from a strip of titanium alloy (6Al-4V) with four strain gauges

bonded to it. These four strain gauges are connected in a full Wheatstone Bridge configuration

with two of them in tensions and the other two in compression. The full bridge configura-

tion is very sensitive and linear to the extension. More information about the design and the